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Fixed rank kriging for very large spatial data sets

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  • Noel Cressie
  • Gardar Johannesson
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    Abstract

    Spatial statistics for very large spatial data sets is challenging. The size of the data set, "n", causes problems in computing optimal spatial predictors such as kriging, since its computational cost is of order . In addition, a large data set is often defined on a large spatial domain, so the spatial process of interest typically exhibits non-stationary behaviour over that domain. A flexible family of non-stationary covariance functions is defined by using a set of basis functions that is fixed in number, which leads to a spatial prediction method that we call fixed rank kriging. Specifically, fixed rank kriging is kriging within this class of non-stationary covariance functions. It relies on computational simplifications when "n" is very large, for obtaining the spatial best linear unbiased predictor and its mean-squared prediction error for a hidden spatial process. A method based on minimizing a weighted Frobenius norm yields best estimators of the covariance function parameters, which are then substituted into the fixed rank kriging equations. The new methodology is applied to a very large data set of total column ozone data, observed over the entire globe, where "n" is of the order of hundreds of thousands. Copyright 2008 Royal Statistical Society.

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

    Volume (Year): 70 (2008)
    Issue (Month): 1 ()
    Pages: 209-226

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    Handle: RePEc:bla:jorssb:v:70:y:2008:i:1:p:209-226

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    Cited by:
    1. Huang, Chunfeng & Zhang, Haimeng & Robeson, Scott M., 2012. "A simplified representation of the covariance structure of axially symmetric processes on the sphere," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1346-1351.
    2. Giovanna Jona Lasinio & Gianluca Mastrantonio & Alessio Pollice, 2013. "Discussing the “big n problem”," Statistical Methods and Applications, Springer, vol. 22(1), pages 97-112, March.
    3. Patrick Gneuss & Wolfgang Schmid & Reimund Schwarze, 2013. "Efficient Approximation of the Spatial Covariance Function for Large Datasets - Analysis of Atmospheric CO2 Concentrations," Discussion Paper Series RECAP15 009, RECAP15, European University Viadrina, Frankfurt (Oder).
    4. Andrew Finley & Sudipto Banerjee & Alan Gelfand, 2012. "Bayesian dynamic modeling for large space-time datasets using Gaussian predictive processes," Journal of Geographical Systems, Springer, vol. 14(1), pages 29-47, January.

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